Upper extremity exoskeletons offer an alternative way to support or rehabilitate patients with physical injury, stroke and spinal cord injury (SCI). This research article presents the kinematic analysis of Exo-First Exoskeleton, which is an 4 DoF upper limb exoskeleton, with the aim of assisting or rehabilitating the shoulder and elbow of the human body. This device covers the entire upper limb of a person, from the clavicle to before the wrist. It is capable of executing motions such as internal-external rotation, adduction-abduction or flexion-extension of the shoulder; and flexion-extension of the elbow. The Denavit-Hartenberg (D-H) method was used to obtain the mathematical model that describes the forward and inverse kinematics of the exoskeleton. Furthermore, the exoskeleton end effector trajectories were obtained using the MATLAB software. The results showed that the proposed design for patients with physical disabilities provides a safer Range of Motion (ROM).